Sb-heterostructure backward diodes have demonstrated their potential as high sensitivity, low-noise, high cutoff frequency and broadband millimeter-wave detectors. This work presents further improvements in detector performance as a result of optimized heterostructure and device design. Structures with ultra-thin 7 Angstrom AlSb barriers have been investigated; these designs resulted in greatly reduced junction resistance and its associated Johnson noise, as well as the potential for doubling of the impedance-matched bandwidth obtainable in imaging applications. Compared to previously demonstrated designs with thicker tunnel barriers, these ultra-thin barrier structures also greatly facilitate design of efficient low-loss matching networks so that this improved bandwidth can be realized in practice. To enhance detector sensitivity, structures with a p-type sheet doping plane in the cathode and an increased anode Al mole fraction of 12% have been studied and resulted in record high curvature, high sensitivity and low noise. In order to understand the underlying physics leading to this excellent detector performance, a theoretical model based on the transfer matrix method and Kane's multi-band formalism has been developed. This model accurately reproduces the measured tunneling current-voltage characteristics for InAs/AlSb/GaSb single barrier interband tunnel structures, and therefore can be a very useful tool for future heterostructure optimization. Based on the experimentally demonstrated performance of the Sb-heterostructure tunnel diode detectors reported here and this model's predictions, the potential performance of a passive unamplified direct detection module appears promising. In particular, the potential system performance of a broadband millimeter-wave radiometer with a planar antenna-coupled Sb-heterostructure detector is evaluated theoretically. A complete fabrication process for realizing discrete detectors as well as planar antenna-coupled detector modules has been developed and used to realize the prototype devices. With the improvement in system design and device performance, the performance of a focal-plane-array style passive millimeter-wave imagers can be greatly improved.